Cover type controlled graph rewriting based parallel system for automated problem solving

Abstract

The invention gives desired algorithmic solutions, even impossible to derive denumerably from preceding ones, as transducers for any kind of problem, e.g. groups of equations or construction puzzles with variables unlimited even by type. The invention treats problems as triples of a mother graph as the subject of the problem, a solving determining recognizer and limit demands for proper solution types. The invention disperses the mother graphs into abstract partial problems regarding chosen interacting rewriting types with mutual relations controlling profoundness in memory hunting, and by bijective partitions creates abstract sisters for those conceptual graphs. As solutions for the examined problems are micros for the parallel transducers of macros of known solving transducers having common parts with substances of those macros and being not necessarily limited to reducing ones. All conceivable solutions are obtained interacting rewrite type being right sides distinct generalized cover renetting, if the mother graph is denumerable and contents in iteration are not expanded. As an exact universal mathematical structure of controlling inventiveness the invention can be considered as the prime algorithm of independently programs inventing machines for problem solving.

1 . A method for automated problem solving comprising the steps:
 i. converting any problem to a triple: the mother graph representing the subject of the problem, the recognizer determining if the problem is solved, and the limit demands for the proper type of solutions, and   ii. A) in order to control comprehensiveness of the searching process choosing the type of the desired interacting cover rewriting system from the set consisting of partition renetting system, generalized partition renetting system, cover renetting system distinct from right sides and generalized cover renetting system distinct from right sides, and
 B) transforming said mother graph by said cover renetting system into the graphs covered with abstract parts, and 
   iii. A) by partition relations constructing cover reversely labelling renetting systems to be applied to said graphs covered with abstract parts thus yielding graphs as the cover result of said generalized partition renetting system for said mother graph, and
 B) producing abstract sisters of said type being in generalized abstraction relation of said type with said graphs covered with abstract parts by
 a) constructing graphs, the amount of the positions of outside arities of which being the same as of said cover result of said interacting cover renetting system for said mother graph, if said type is partition renetting system or cover renetting system distinct from right sides, and 
 b) constructing graphs a substance of which has a partition being in bisection with a partition in a substance of said cover result of said interacting cover renetting system for said mother graph, if said type is generalized cover renetting system distinct from right sides, and 
 
   iv. A) applying known transducers for substances of said abstract sisters, the nodes of said known transducers being rewrite systems and said known transducers solving problems the mother graphs of which have common parts with said substances, and
 B) a) constructing generalized altering macros for said known transducers, and
 b) simultaneously for rule after rule in said macros constructing altering transducers parallel with said macros, and 
 
 C) applying said parallel altering transducers for said cover result for said mother graph, and on the other hand applying said macros of said known transducers for said abstract sisters of said type to get graphs being in said generalized abstraction relation with each other, and 
   V. A) a) constructing micros for said parallel altering transducers, and
 b) as the right solutions for a given problem choosing those ones of said micros which fulfil said limit demands and produce graphs recognized by said recognizer, and 
   B) in the case said mother graph is denumerable, those said right solutions containing for said given problem all those solutions which are not contents expanding.